Related papers: Use of Signed Permutations in Cryptography
Homomorphic encryption is a method used in cryptopgraphy to create programs that can interact with encrypted data without ever leaving the data in the clear. This has many potential applications in cybersecurity. This paper uses…
Confidentiality and Integrity are two paramount objectives in the evaluation of information and communication technology. In this paper, we propose an arithmetic approach for designing asymmetric key cryptography. Our method is based on the…
The braid group is an important non commutative group, at the same time, it is an important tool in quantum field theory with better topological structure, and often used as a research carrier for anti-quantum cryptographic algorithms. This…
During the past decades, there is a great popularity employing nonlinear dynamics and permutation-substitution architecture for image encryption. There are three primary procedures in such encryption schemes, the key schedule module for…
We've been able to show recently that Permutable Chebyshev polynomials (T polynomials) defined over the field of real numbers can be used to create a Diffie-Hellman-like key exchange algorithm and certificates. The cryptosystem was…
We study the combinatorial equivalence of separable elements in types $A$ and $B$. A bijection is constructed from the set of separable permutations in the symmetric group $S_{n+1}$ to the set of separable signed permutations in the…
In this paper, we prove an important cryptographic property of $PE$-transformation proposed elsewhere. If $PE$-transformation is used as encrypting function then after $n$ applications of it on arbitrary message the distribution of…
In response to the evolving landscape of quantum computing and the escalating vulnerabilities in classical cryptographic systems, our paper introduces a unified cryptographic framework. Rooted in the innovative work of Kuang et al., we…
In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of…
In this paper, we study groups of automorphisms of algebraic systems over a set of $p$-adic integers with different sets of arithmetic and coordinate-wise logical operations and congruence relations modulo $p^k,$ $k\ge 1.$ The main result…
Since fully homomorphic encryption and homomorphically encrypted computing preserve algebraic identities such as 2*2=2+2, a natural question is whether this extremely utilitarian feature also sets up cryptographic attacks that use the…
We review new frontiers in information security technologies in communications and distributed storage technologies with the use of classical, quantum, hybrid classical-quantum, and post-quantum cryptography. We analyze the current…
Threshold cryptography is a powerful and well-known technique with many applications to systems relying on distributed trust. It has recently emerged also as a solution to challenges in blockchain: frontrunning prevention, managing wallet…
This paper presents results on generalized public key cryptography with exponentials modulo primes and composite numbers where the mapping is not one-to-one and the uniqueness is achieved by additional side information. Such transformations…
Post-quantum cryptography (PQC) attempts to find cryptographic protocols resistant to attacks using for instance Shor's polynomial time algorithm for numerical field problems like integer factorization (IFP) or the discrete logarithm (DLP).…
We propose an adaptive threshold multi secret sharing scheme based solely on cryptographically secure hash functions. We show that the proposed scheme is also: perfect, ideal, verifiable, and proactive. Moreover the proposed scheme has a…
Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…
Two variations of the McEliece cryptosystem are presented. The first one is based on a relaxation of the column permutation in the classical McEliece scrambling process. This is done in such a way that the Hamming weight of the error, added…
This paper studies a variant of the McEliece cryptosystem able to ensure that the code used as the public key is no longer permutation-equivalent to the secret code. This increases the security level of the public key, thus opening the way…
With the development of machine learning, it is difficult for a single server to process all the data. So machine learning tasks need to be spread across multiple servers, turning the centralized machine learning into a distributed one.…